Q : 1     Fill in the blanks in the following table, given that a is the first term, d the common  difference and \small a_n  the \small nth term of the AP:                                                                             

                

  a d n \small a_n

(i)

(ii)

(iii)

(iv)

(v)

7

\small -18

\small ...

\small -18.9

\small 3.5

3

\small ...

\small -3

\small 2.5

0

8

10

18

\small ...

105

\small ...

0

\small -5

\small 3.6

\small ...

 

Answers (1)

(i)
It is given that 
a=7, d = 3 , n = 8
Now,  we know that
a_n = a+(n-1)d
a_8 = 7+(8-1)3= 7+7\times 3 = 7+21 = 28
Therefore, 
a_8 = 28

(ii)
It is given that 
a=-18, n = 10, a_{10} = 0
Now,  we know that
a_n = a+(n-1)d
a_{10} = -18+(10-1)d
0 +18=9d
d = \frac{18}{9}=2
(iii)
It is given that 
d=-3, n = 18, a_{18} = -5
Now,  we know that
a_n = a+(n-1)d
a_{18} = a+(18-1)(-3)
-5=a+17\times (-3)
a = 51-5 = 46
Therefore, 
a = 46

(iv)
It is given that 
a=-18.9, d = 2.5, a_{n} = 3.6
Now,  we know that
a_n = a+(n-1)d
a_{n} = -18.9+(n-1)2.5
3.6+18.9= 2.5n-2.5
n = \frac{22.5+2.5}{2.5}= \frac{25}{2.5}= 10
Therefore, 
n = 10

(v)
It is given that 
a=3.5, d = 0, n = 105
Now,  we know that
a_n = a+(n-1)d
a_{105} = 3.5+(105-1)0
a_{105} = 3.5
Therefore, 
a_{105} = 3.5

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